ALGEBRA Notes, Quizzes & Revision
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ALGEBRA
Topic: topic_name_replace | Subject: subject_replace | Age group: age_replace
Aligned to Kenyan curriculum expectations for age_replace learners (basic algebraic skills useful for KCSE foundation topics).
Learning outcomes
- Understand and use symbols (variables) to represent numbers.
- Simplify algebraic expressions using like terms and basic operations.
- Solve simple linear equations in one variable.
- Perform substitution into formulae and evaluate results.
Key concepts & notation
- Variable โ a symbol (often x, y) representing a number. Example: x, y.
- Term โ a number, a variable, or a product of numbers and variables (e.g., 3, x, 4x).
- Coefficient โ the number multiplied by a variable, e.g., in 5x the coefficient is 5.
- Like terms โ terms with the same variable parts (e.g., 3x and โ2x).
- Expression โ combination of terms (e.g., 2x + 3).
- Equation โ a statement that two expressions are equal (e.g., 2x + 3 = 11).
1. Simplifying expressions
Steps:
- Collect like terms (add or subtract coefficients of same variable).
- Perform any multiplications or divisions first (use distributive law to expand brackets).
Example 1:
Simplify: 3x + 5x โ 2
3x + 5x โ 2 = (3 + 5)x โ 2 = 8x โ 2
Example 2 (expand using distributive law):
Expand: 4(x + 3)
4(x + 3) = 4รx + 4ร3 = 4x + 12
2. Solving simple linear equations
Principle: Do the same operation to both sides to isolate the variable.
Example 3:
Solve: 2x + 5 = 17
Subtract 5 from both sides: 2x = 12
Divide both sides by 2: x = 6
Divide both sides by 2: x = 6
Example 4 (variable on both sides):
Solve: 3x โ 4 = x + 8
Subtract x from both sides: 2x โ 4 = 8
Add 4 to both sides: 2x = 12
Divide by 2: x = 6
Add 4 to both sides: 2x = 12
Divide by 2: x = 6
3. Substitution into formulae
To evaluate a formula, replace each variable with its given value and compute.
Example 5:
If A = 2x + 3 and x = 4, then A = 2(4) + 3 = 8 + 3 = 11
4. Worked problem (context)
Mwangi sells sugar packets. He sells x packets per day. His daily income (in KSh) is given by I = 50x + 200 (50 sh per packet plus 200 sh fixed). If Mwangi earned KSh 1,200 in one day, find x.
50x + 200 = 1200
50x = 1200 โ 200 = 1000
x = 1000 รท 50 = 20 packets
Answer: Mwangi sold 20 packets.
50x = 1200 โ 200 = 1000
x = 1000 รท 50 = 20 packets
Practice questions
- Simplify: 6y โ 2y + 9.
- Expand: 3(2x โ 4).
- Solve: 5x + 7 = 32.
- Solve: 4(a โ 1) = 2a + 6.
- If P = 3n + 5 and P = 23, find n.
Answers
- 6y โ 2y + 9 = 4y + 9.
- 3(2x โ 4) = 6x โ 12.
- 5x + 7 = 32 โ 5x = 25 โ x = 5.
- 4(a โ 1) = 2a + 6 โ 4a โ 4 = 2a + 6 โ 2a = 10 โ a = 5.
- 3n + 5 = 23 โ 3n = 18 โ n = 6.
Study tips:
- Always perform the same operation to both sides of an equation.
- Check your answers by substitution.
- Use simple Kenyan examples (prices, quantities, distances) to make algebra meaningful.